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# Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case.

 dc.creator Fernández-Nieto, Enrique D. dc.creator Gallardo, José M. dc.creator Vigneaux, Paul dc.date.accessioned 2015-12-23T11:49:52Z dc.date.available 2015-12-23T11:49:52Z dc.date.issued 2014 dc.identifier.issn 1090-2716 es dc.identifier.uri http://hdl.handle.net/11441/32180 dc.description.abstract This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non-trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated with the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez–Moreno) to discretize the problem. To be able to accurately simulate the stopping behavior of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances. es dc.format application/pdf es dc.language.iso eng es dc.publisher Elsevier es dc.relation.ispartof Journal of Computational Physics, 264, pp. 55–90 es dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional * dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ * dc.subject Viscoplastic es dc.subject Shallow water es dc.subject Well-balanced es dc.subject Finite volume es dc.subject Variational inequality es dc.subject Bingham es dc.title Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case. es dc.type info:eu-repo/semantics/article es dc.type.version info:eu-repo/semantics/submittedVersion es dc.rights.accessrights info:eu-repo/semantics/openAccess es dc.contributor.affiliation Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) es dc.relation.publisherversion doi:10.1016/j.jcp.2014.01.026 es dc.relation.publisherversion http://dx.doi.org/10.1016/j.jcp.2014.01.026 dc.identifier.doi 10.1016/j.jcp.2014.01.026 es dc.identifier.idus https://idus.us.es/xmlui/handle/11441/32180
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